where one exploits that \(\partial _t \phi =-v \partial _x \phi \)  and \(\partial _{tt} \phi = - v \partial _{tx} \phi )\) . Such approach is often called Lax-Wendroff procedure [1]}. Opposite to its standard form when all time derivatives in (REF ) are replaced by spatial derivatives using the equation (REF ), we allow also the mixed derivatives in (REF ).
